Last updated

In physics, an electronvolt (symbol eV, also written electron-volt and electron volt) is the measure of an amount of kinetic energy gained by a single electron accelerating from rest through an electric potential difference of one volt in vacuum. When used as a unit of energy, the numerical value of 1 eV in joules (symbol J) is equivalent to the numerical value of the charge of an electron in coulombs (symbol C). Under the 2019 redefinition of the SI base units, this sets 1 eV equal to the exact value 1.602176634×10−19 J. [1]


Historically, the electronvolt was devised as a standard unit of measure through its usefulness in electrostatic particle accelerator sciences, because a particle with electric charge q gains an energy E = qV after passing through a voltage of V. Since q must be an integer multiple of the elementary charge e for any isolated particle, the gained energy in units of electronvolts conveniently equals that integer times the voltage.

It is a common unit of energy within physics, widely used in solid state, atomic, nuclear, and particle physics, and high-energy astrophysics. It is commonly used with SI prefixes milli-, kilo-, mega-, giga-, tera-, peta- or exa- (meV, keV, MeV, GeV, TeV, PeV and EeV respectively). In some older documents, and in the name Bevatron, the symbol BeV is used, which stands for billion (109) electronvolts; it is equivalent to the GeV.


An electronvolt is the amount of kinetic energy gained or lost by a single electron accelerating from rest through an electric potential difference of one volt in vacuum. Hence, it has a value of one volt, 1 J/C, multiplied by the elementary charge e = 1.602176634×10−19 C. [2] Therefore, one electronvolt is equal to 1.602176634×10−19 J. [1]

The electronvolt (eV) is a unit of energy, but is not an SI unit. The SI unit of energy is the joule (J).

Relation to other physical properties and units

MeasurementUnitSI value of unit
Energy eV1.602176634×10−19 J
Mass eV/c21.78266192×10−36 kg
Momentum eV/c5.34428599×10−28 kg·m/s
Temperature eV/kB1.160451812×104 K
Time ħ/eV6.582119×10−16 s
Distance ħc/eV1.97327×10−7 m


By mass–energy equivalence, the electronvolt corresponds to a unit of mass. It is common in particle physics, where units of mass and energy are often interchanged, to express mass in units of eV/c2, where c is the speed of light in vacuum (from E = mc2). It is common to informally express mass in terms of eV as a unit of mass, effectively using a system of natural units with c set to 1. [3] The kilogram equivalent of 1 eV/c2 is:

For example, an electron and a positron, each with a mass of 0.511 MeV/c2, can annihilate to yield 1.022 MeV of energy. A proton has a mass of 0.938 GeV/c2. In general, the masses of all hadrons are of the order of 1 GeV/c2, which makes the GeV/c2 a convenient unit of mass for particle physics: [4]

1 GeV/c2 = 1.78266192×10−27 kg.

The atomic mass constant (mu), one twelfth of the mass a carbon-12 atom, is close to the mass of a proton. To convert to electronvolt mass-equivalent, use the formula:

mu = 1 Da = 931.4941 MeV/c2 = 0.9314941 GeV/c2.


By dividing a particle's kinetic energy in electronvolts by the fundamental constant c (the speed of light), one can describe the particle's momentum in units of eV/c. [5] In natural units in which the fundamental velocity constant c is numerically 1, the c may informally be omitted to express momentum as electronvolts.

The energy-momentum relation in natural units,
{\displaystyle E^{2}=p^{2}+m_{0}^{2}}
, is a Pythagorean equation that can be visualized as a right triangle where the total energy
{\displaystyle E}
is the hypotenuse and the momentum
{\displaystyle p}
and rest mass
{\displaystyle m_{0}}
are the two legs. Einstein-triangle-in-natural-units.svg
The energy–momentum relation in natural units, , is a Pythagorean equation that can be visualized as a right triangle where the total energy is the hypotenuse and the momentum and rest mass are the two legs.

The energy momentum relation

in natural units (with )

is a Pythagorean equation. When a relatively high energy is applied to a particle with relatively low rest mass, it can be approximated as in high-energy physics such that an applied energy in units of eV conveniently results in an approximately equivalent change of momentum in units of eV/c.

The dimensions of momentum units are T−1LM. The dimensions of energy units are T−2L2M. Dividing the units of energy (such as eV) by a fundamental constant (such as the speed of light) that has units of velocity (T−1L) facilitates the required conversion for using energy units to describe momentum.

For example, if the momentum p of an electron is said to be 1 GeV, then the conversion to MKS system of units can be achieved by:


In particle physics, a system of natural units in which the speed of light in vacuum c and the reduced Planck constant ħ are dimensionless and equal to unity is widely used: c = ħ = 1. In these units, both distances and times are expressed in inverse energy units (while energy and mass are expressed in the same units, see mass–energy equivalence). In particular, particle scattering lengths are often presented in units of inverse particle masses.

Outside this system of units, the conversion factors between electronvolt, second, and nanometer are the following:

The above relations also allow expressing the mean lifetime τ of an unstable particle (in seconds) in terms of its decay width Γ (in eV) via Γ = ħ/τ. For example, the
has a lifetime of 1.530(9)  picoseconds, mean decay length is = 459.7 μm, or a decay width of (4.302±25)×10−4 eV.

Conversely, the tiny meson mass differences responsible for meson oscillations are often expressed in the more convenient inverse picoseconds.

Energy in electronvolts is sometimes expressed through the wavelength of light with photons of the same energy:


In certain fields, such as plasma physics, it is convenient to use the electronvolt to express temperature. The electronvolt is divided by the Boltzmann constant to convert to the Kelvin scale:

where kB is the Boltzmann constant.

The kB is assumed when using the electronvolt to express temperature, for example, a typical magnetic confinement fusion plasma is 15 keV (kiloelectronvolt), which is equal to 174 MK (megakelvin).

As an approximation: kBT is about 0.025 eV (≈ 290 K/11604 K/eV) at a temperature of 20 °C.


Energy of photons in the visible spectrum in eV Colors in eV.svg
Energy of photons in the visible spectrum in eV
Graph of wavelength (nm) to energy (eV) EV to nm vis.png
Graph of wavelength (nm) to energy (eV)

The energy E, frequency v, and wavelength λ of a photon are related by

where h is the Planck constant, c is the speed of light. This reduces to [6]

A photon with a wavelength of 532 nm (green light) would have an energy of approximately 2.33 eV. Similarly, 1 eV would correspond to an infrared photon of wavelength 1240 nm or frequency 241.8 THz.

Scattering experiments

In a low-energy nuclear scattering experiment, it is conventional to refer to the nuclear recoil energy in units of eVr, keVr, etc. This distinguishes the nuclear recoil energy from the "electron equivalent" recoil energy (eVee, keVee, etc.) measured by scintillation light. For example, the yield of a phototube is measured in phe/keVee (photoelectrons per keV electron-equivalent energy). The relationship between eV, eVr, and eVee depends on the medium the scattering takes place in, and must be established empirically for each material.

Energy comparisons

Photon frequency vs. energy particle in electronvolts. The energy of a photon varies only with the frequency of the photon, related by speed of light constant. This contrasts with a massive particle of which the energy depends on its velocity and rest mass. Legend
g: Gamma rays
MIR: Mid infrared
HF: High freq.
HX: Hard X-rays
FIR: Far infrared
MF: Medium freq.
SX: Soft X-rays
Radio waves
LF: Low freq.
EUV: Extreme ultraviolet
EHF: Extremely high freq.
VLF: Very low freq.
NUV: Near ultraviolet
SHF: Super high freq.
VF/ULF: Voice freq.
Visible light
UHF: Ultra high freq.
SLF: Super low freq.
NIR: Near Infrared
VHF: Very high freq.
ELF: Extremely low freq.
Freq: Frequency Light spectrum.svg
Photon frequency vs. energy particle in electronvolts. The energy of a photon varies only with the frequency of the photon, related by speed of light constant. This contrasts with a massive particle of which the energy depends on its velocity and rest mass. Legend
γ: Gamma rays MIR: Mid infraredHF: High freq.
HX: Hard X-rays FIR: Far infraredMF: Medium freq.
SX: Soft X-rays Radio waves LF: Low freq.
EUV: Extreme ultraviolet EHF: Extremely high freq. VLF: Very low freq.
NUV: Near ultraviolet SHF: Super high freq. VF/ULF: Voice freq.
Visible light UHF: Ultra high freq. SLF: Super low freq.
NIR: Near Infrared VHF: Very high freq. ELF: Extremely low freq.
Freq: Frequency
5.25×1032 eVtotal energy released from a 20  kt nuclear fission device
12.2 R eV (1.22×1028 eV)the Planck energy
10 Y eV (1×1025 eV)approximate grand unification energy
~624 E eV (6.24×1020 eV)energy consumed by a single 100-watt light bulb in one second (100 W = 100 J/s6.24×1020 eV/s)
300 E eV (3×1020 eV = ~50  J )The first ultra-high-energy cosmic ray particle observed, the so-called Oh-My-God particle. [10]
2 PeVtwo petaelectronvolts, the highest-energy neutrino detected by the IceCube neutrino telescope in Antarctica [11]
14 TeVdesigned proton center-of-mass collision energy at the Large Hadron Collider (operated at 3.5 TeV since its start on 30 March 2010, reached 13 TeV in May 2015)
1 TeVa trillion electronvolts, or 1.602×10−7 J, about the kinetic energy of a flying mosquito [12]
172 GeVrest energy of top quark, the heaviest measured elementary particle
125.1±0.2 GeVenergy corresponding to the mass of the Higgs boson, as measured by two separate detectors at the LHC to a certainty better than 5 sigma [13]
210 MeVaverage energy released in fission of one Pu-239 atom
200 MeVapproximate average energy released in nuclear fission fission fragments of one U-235 atom.
105.7 MeVrest energy of a muon
17.6 MeVaverage energy released in the nuclear fusion of deuterium and tritium to form He-4; this is 0.41 PJ per kilogram of product produced
2 MeVapproximate average energy released in a nuclear fission neutron released from one U-235 atom.
1.9 MeVrest energy of up quark, the lowest mass quark.
1 MeV (1.602×10−13 J)about twice the rest energy of an electron
1 to 10 keVapproximate thermal temperature, , in nuclear fusion systems, like the core of the sun, magnetically confined plasma, inertial confinement and nuclear weapons
13.6 eVthe energy required to ionize atomic hydrogen; molecular bond energies are on the order of 1 eV to 10 eV per bond
1.6 eV to 3.4 eVthe photon energy of visible light
1.1 eVenergy required to break a covalent bond in silicon
720 meVenergy required to break a covalent bond in germanium
< 120 meVapproximate rest energy of neutrinos (sum of 3 flavors) [14]
25 meV thermal energy, , at room temperature; one air molecule has an average kinetic energy 38 meV
230 μeVthermal energy, , of the cosmic microwave background

Per mole

One mole of particles given 1 eV of energy each has approximately 96.5 kJ of energy – this corresponds to the Faraday constant (F96485 C⋅mol−1), where the energy in joules of n moles of particles each with energy E eV is equal to E·F·n.

See also

Related Research Articles

<span class="mw-page-title-main">Kinetic energy</span> Energy of a moving physical body

In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body when decelerating from its current speed to a state of rest. Formally, a kinetic energy is any term in a system's Lagrangian which includes a derivative with respect to time.

<span class="mw-page-title-main">Torque</span> Physics concept

In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment of force. It represents the capability of a force to produce change in the rotational motion of the body. The concept originated with the studies by Archimedes of the usage of levers, which is reflected in his famous quote: "Give me a lever and a place to stand and I will move the Earth". Just as a linear force is a push or a pull, a torque can be thought of as a twist to an object around a specific axis. Torque is defined as the product of the magnitude of the perpendicular component of the force and the distance of the line of action of a force from the point around which it is being determined. The law of conservation of energy can also be used to understand torque. The symbol for torque is typically , the lowercase Greek letter tau. When being referred to as moment of force, it is commonly denoted by M.

<span class="mw-page-title-main">Pair production</span> Interaction of a photon with matter resulting into creation of electron-positron pair

Pair production is the creation of a subatomic particle and its antiparticle from a neutral boson. Examples include creating an electron and a positron, a muon and an antimuon, or a proton and an antiproton. Pair production often refers specifically to a photon creating an electron–positron pair near a nucleus. As energy must be conserved, for pair production to occur, the incoming energy of the photon must be above a threshold of at least the total rest mass energy of the two particles created. Conservation of energy and momentum are the principal constraints on the process. All other conserved quantum numbers of the produced particles must sum to zero – thus the created particles shall have opposite values of each other. For instance, if one particle has electric charge of +1 the other must have electric charge of −1, or if one particle has strangeness of +1 then another one must have strangeness of −1.

In spectroscopy, the Rydberg constant, symbol for heavy atoms or for hydrogen, named after the Swedish physicist Johannes Rydberg, is a physical constant relating to the electromagnetic spectra of an atom. The constant first arose as an empirical fitting parameter in the Rydberg formula for the hydrogen spectral series, but Niels Bohr later showed that its value could be calculated from more fundamental constants via his Bohr model.

In thermodynamics, the chemical potential of a species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potential of a species in a mixture is defined as the rate of change of free energy of a thermodynamic system with respect to the change in the number of atoms or molecules of the species that are added to the system. Thus, it is the partial derivative of the free energy with respect to the amount of the species, all other species' concentrations in the mixture remaining constant. When both temperature and pressure are held constant, and the number of particles is expressed in moles, the chemical potential is the partial molar Gibbs free energy. At chemical equilibrium or in phase equilibrium, the total sum of the product of chemical potentials and stoichiometric coefficients is zero, as the free energy is at a minimum. In a system in diffusion equilibrium, the chemical potential of any chemical species is uniformly the same everywhere throughout the system.

<span class="mw-page-title-main">Electrostatics</span> Study of stationary electric charge

Electrostatics is a branch of physics that studies electric charges at rest.

In particle physics, the W and Z bosons are vector bosons that are together known as the weak bosons or more generally as the intermediate vector bosons. These elementary particles mediate the weak interaction; the respective symbols are
, and
. The
 bosons have either a positive or negative electric charge of 1 elementary charge and are each other's antiparticles. The
 boson is electrically neutral and is its own antiparticle. The three particles each have a spin of 1. The
 bosons have a magnetic moment, but the
has none. All three of these particles are very short-lived, with a half-life of about 3×10−25 s. Their experimental discovery was pivotal in establishing what is now called the Standard Model of particle physics.

<span class="mw-page-title-main">Magnetic moment</span> Magnetic strength and orientation of an object that produces a magnetic field

In electromagnetism, the magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include loops of electric current, permanent magnets, elementary particles, various molecules, and many astronomical objects.

<span class="mw-page-title-main">Coupling constant</span> Parameter describing the strength of a force

In physics, a coupling constant or gauge coupling parameter, is a number that determines the strength of the force exerted in an interaction. Originally, the coupling constant related the force acting between two static bodies to the "charges" of the bodies divided by the distance squared, , between the bodies; thus: in for Newtonian gravity and in for electrostatic. This description remains valid in modern physics for linear theories with static bodies and massless force carriers.

<span class="mw-page-title-main">Lawson criterion</span> Criterion for igniting a nuclear fusion chain reaction

The Lawson criterion is a figure of merit used in nuclear fusion research. It compares the rate of energy being generated by fusion reactions within the fusion fuel to the rate of energy losses to the environment. When the rate of production is higher than the rate of loss, the system will produce net energy. If enough of that energy is captured by the fuel, the system will become self-sustaining and is said to be ignited.

In physics, the gyromagnetic ratio of a particle or system is the ratio of its magnetic moment to its angular momentum, and it is often denoted by the symbol γ, gamma. Its SI unit is the radian per second per tesla (rad⋅s−1⋅T−1) or, equivalently, the coulomb per kilogram (C⋅kg−1).

In atomic physics, the electron magnetic moment, or more specifically the electron magnetic dipole moment, is the magnetic moment of an electron resulting from its intrinsic properties of spin and electric charge. The value of the electron magnetic moment is −9.2847647043(28)×10−24 J⋅T−1. The electron magnetic moment has been measured to an accuracy of 1.7×10−13 relative to the Bohr magneton.

<span class="mw-page-title-main">Weinberg angle</span> Angle characterizing electroweak symmetry breaking

The weak mixing angle or Weinberg angle is a parameter in the Weinberg–Salam theory of the electroweak interaction, part of the Standard Model of particle physics, and is usually denoted as θW. It is the angle by which spontaneous symmetry breaking rotates the original
vector boson plane, producing as a result the
 boson, and the photon. Its measured value is slightly below 30°, but also varies, very slightly increasing, depending on how high the relative momentum of the particles involved in the interaction is that the angle is used for.

<span class="mw-page-title-main">Neutrinoless double beta decay</span>

The neutrinoless double beta decay (0νββ) is a commonly proposed and experimentally pursued theoretical radioactive decay process that would prove a Majorana nature of the neutrino particle. To this day, it has not been found.

<span class="mw-page-title-main">Plasma parameters</span>

Plasma parameters define various characteristics of a plasma, an electrically conductive collection of charged particles that responds collectively to electromagnetic forces. Plasma typically takes the form of neutral gas-like clouds or charged ion beams, but may also include dust and grains. The behaviour of such particle systems can be studied statistically.

Energy is defined via work, so the SI unit of energy is the same as the unit of work – the joule (J), named in honour of James Prescott Joule and his experiments on the mechanical equivalent of heat. In slightly more fundamental terms, 1 joule is equal to 1 newton metre and, in terms of SI base units

A g-factor is a dimensionless quantity that characterizes the magnetic moment and angular momentum of an atom, a particle or the nucleus. It is essentially a proportionality constant that relates the different observed magnetic moments μ of a particle to their angular momentum quantum numbers and a unit of magnetic moment, usually the Bohr magneton or nuclear magneton.

In strong-field laser physics, ponderomotive energy is the cycle-averaged quiver energy of a free electron in an electromagnetic field.

<span class="mw-page-title-main">Classical mechanics</span> Description of large objects physics

Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical mechanics, if the present state is known, it is possible to predict how it will move in the future (determinism), and how it has moved in the past (reversibility).

The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalence, the relationship between mass and frequency. Specifically, a photon's energy is equal to its frequency multiplied by the Planck constant. The constant is generally denoted by . The reduced Planck constant, or Dirac constant, equal to the constant divided by , is denoted by .


  1. 1 2 "2018 CODATA Value: electron volt". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  2. "2018 CODATA Value: elementary charge". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  3. Barrow, J. D. (1983). "Natural Units Before Planck". Quarterly Journal of the Royal Astronomical Society. 24: 24. Bibcode:1983QJRAS..24...24B.
  4. Gron Tudor Jones. "Energy and momentum units in particle physics" (PDF). Indico.cern.ch. Retrieved 5 June 2022.
  5. "Units in particle physics". Associate Teacher Institute Toolkit. Fermilab. 22 March 2002. Archived from the original on 14 May 2011. Retrieved 13 February 2011.
  6. "CODATA Value: Planck constant in eV s". Archived from the original on 22 January 2015. Retrieved 30 March 2015.
  7. What is Light? Archived December 5, 2013, at the Wayback Machine UC Davis lecture slides
  8. Elert, Glenn. "Electromagnetic Spectrum, The Physics Hypertextbook". hypertextbook.com. Archived from the original on 2016-07-29. Retrieved 2016-07-30.
  9. "Definition of frequency bands on". Vlf.it. Archived from the original on 2010-04-30. Retrieved 2010-10-16.
  10. Open Questions in Physics. Archived 2014-08-08 at the Wayback Machine German Electron-Synchrotron. A Research Centre of the Helmholtz Association. Updated March 2006 by JCB. Original by John Baez.
  11. "A growing astrophysical neutrino signal in IceCube now features a 2-PeV neutrino". Archived from the original on 2015-03-19.
  12. Glossary Archived 2014-09-15 at the Wayback Machine - CMS Collaboration, CERN
  13. ATLAS; CMS (26 March 2015). "Combined Measurement of the Higgs Boson Mass in pp Collisions at √s=7 and 8 TeV with the ATLAS and CMS Experiments". Physical Review Letters. 114 (19): 191803. arXiv: 1503.07589 . Bibcode:2015PhRvL.114s1803A. doi: 10.1103/PhysRevLett.114.191803 . PMID   26024162.
  14. Mertens, Susanne (2016). "Direct neutrino mass experiments". Journal of Physics: Conference Series. 718 (2): 022013. arXiv: 1605.01579 . Bibcode:2016JPhCS.718b2013M. doi:10.1088/1742-6596/718/2/022013. S2CID   56355240.